A note on subvarieties of powers of OT-manifolds

It is shown that the space of finite-to-finite holomorphic correspondences on an OT-manifold is discrete. When the OT-manifold has no proper infinite complex-analytic subsets, it then follows by known model-theoretic results that its cartesian powers have no interesting complex-analytic families of subvarieties. The methods of proof, which are similar to [Moosa, Moraru, and Toma ``An essentially saturated surface not of Kähler-type", {\em Bull. of the LMS}, 40(5):845–854, 2008], require studying finite unramified covers of OT-manifolds.